Algebra Examples

$\frac{x^{2} - 4}{x^{2} - 9}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $4$ as $2^{2}$ .

$\frac{x^{2} - 2^{2}}{x^{2} - 9}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$\frac{(x + 2) (x - 2)}{x^{2} - 9}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{(x + 2) (x - 2)}{x^{2} - 3^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{(x + 2) (x - 2)}{(x + 3) (x - 3)}$